MC-CDMA downlink transmission method

ABSTRACT

The invention concerns a transmission method for transmitting a plurality of symbols from a base station of a MC-CDMA telecommunication system to a plurality (K) of users, each symbol (d k ) to be transmitted to a user being spread with a coding sequence (c k (l), c k   ext (l) over a plurality (L) of carriers (l) to produce a plurality of corresponding frequency component, said base station being provided with a plurality (M) of antenna elements. According to the invention, each frequency component produced by a symbol of a user (k) is weighted by a plurality (M) of weighting complex coefficients (w k *(l,m),m=1, . . , M) to obtain a plurality (LM) of weighted frequency components (z k   m (l)), each weighting coefficient being relative to a user (k), a carrier (l) and an antenna element (m) and said plurality of weighting coefficients being determined from estimates of the channel coefficients (h k (l,m)) of the downlink transmission channels between each antenna element and each user for each carrier frequency.

The present invention concerns a method of transmission from a basestation of a MC-CDMA telecommunication system to a plurality of usersthereof

MC-CDMA has been receiving widespread interest for wireless broadbandmultimedia applications. Multi-Carrier Code Division Multiple Access(MC-CDMA) combines OFDM (Orthogonal Frequency Division Multiplex)modulation and the CDMA multiple access technique. This multiple accesstechnique was proposed for the first time by N. Yee et al. in thearticle entitled “Multicarrier CDMA in indoor wireless radio networks”which appeared in Proceedings of PIMRC'93, Vol. 1, pages 109-113, 1993.The developments of this technique were reviewed by S. Hara et al. inthe article entitled “Overview of Multicarrier CDMA” published in IEEECommunication Magazine, pages 126-133, December 1997.

Unlike DS-CDMA (Direct Spread Code Division Multiple Access), in whichthe signal of each user is multiplied in the time domain in order tospread its frequency spectrum, the signature here multiplies the signalin the frequency domain, each element of the signature multiplying thesignal of a different sub-carrier.

In general, MC-CDMA combines the advantageous features of CDMA and OFDM,Le. high spectral efficiency, multiple access capabilities, robustnessin presence of frequency selective channels, high flexibility,narrow-band interference rejection, simple one-tap equalisation, etc.

FIG. 1 illustrates schematically the structure of a MC-CDMA transmittertransmitting a plurality of MC-CDMA symbols to a plurality K of users.For example, we suppose that the transmitter is located in a basestation of a MC-CDMA transmission system and transmits MC-CDMA symbolsto a plurality of users over a plurality of downlink transmissionchannels.

Let d_(k)(n) be a complex symbol to be transmitted from the base stationto user k at time nT, where d_(k)(n) belongs to the modulation alphabetand let denote {square root}{square root over (Pt_(k))} the transmissionamplitude coefficient relative to this symbol, where Pt_(k) is the powerof transmission associated to user k during the transmission frame towhich d_(k)(n) belongs. The complex value {square root}{square root over(Pt_(k))} d_(k)(n) is first multiplied at multiplier 110 _(k) by aspreading sequence denoted c_(k)(l). The spreading sequence consists ofN “chips”, each “chip” being of duration T_(c), the total duration ofthe spreading sequence corresponding to a symbol period T. We assumeotherwise specified in the following that a single spreading sequence isallocated for the transmission to a user. In general, however, aplurality of orthogonal spreading sequences (multi-code allocation) canbe allocated to a given user according to the data rate required. Inorder to mitigate intra-cell interference, the spreading sequences arechosen orthogonal.

The result of the multiplication of the complex value {squareroot}{square root over (Pt_(k))}.d_(k)(n), hereinafter simply denoted{square root}{square root over (Pt_(k))}.d_(k), by the elements of thespreading sequence for user k gives N complex values demultiplexed indemultiplexer 120 _(k) over a subset of N frequencies of an OFDMmultiplex. In general, the number N of frequencies of said subset is asub-multiple of the number L of frequencies of the OFDM multiplex. Weassume in the following that L=N and denote c_(k)(l)=c_(k)(lT_(c)), l=1,. . , , L the values of the spreading sequence elements for user k. Theblock of complex values demultiplexed in 120 _(k) is then subjected toan inverse fast Fourier transformation (IFFT) in the module 130 _(k). Inorder to prevent intersymbol interference, a guard interval of lengthtypically greater than the duration of the impulse response of thetransmission channel, is added to the MC-CDMA symbol. This is achievedin practice by adding a prefix (denoted Δ) identical to the end of thesaid symbol. After being serialised in the parallel to serial converter140 _(k) and converted into an analogue signal (conversion not shown)the MC-CDMA symbol S_(k) to be sent to user k is added in adder 150 tothe similar MC-CDMA symbols S_(k). to be transmitted to the other usersk′≈k. The resulting sum S is then filtered and RF frequency up-converted(not shown) before being transmitted by the base station. The MC-CDMAmethod can essentially be regarded as a spreading in the spectral domain(before IFFT) followed by an OFDM modulation.

The signal S_(k) at time t which is supplied to the adder 150 beforebeing transmitted over the downlink transmission channel can thereforebe written, if we omit the prefix: $\begin{matrix}{{S_{k}(t)} = {{d_{k} \cdot \sqrt{P\quad t_{k}} \cdot {\sum\limits_{l = 1}^{L}{{c_{k}(l)}{\exp\left( {{j \cdot 2}\pi\quad f_{l}t} \right)}\quad{for}\quad n\quad T}}} \leq t < {\left( {n + 1} \right)T}}} & (1)\end{matrix}$where f_(t)=((l−1)−L.2)/T, l=1, . . . , L are the frequencies of theOFDM multiplex. More precisely, it should be understood that thetransmitted signal is in fact Re(S_(k)(t) exp (j2σF₀t)) where Re(.)stands for the real part and F₀ is the RF carrier frequency. In otherwords, S_(k)(t) is the complex envelope of the transmitted signal.

The resulting sum signal S can be written at time t: $\begin{matrix}{{S(t)} = {{\sum\limits_{k = 1}^{K}{d_{k} \cdot \sqrt{P\quad t_{k}} \cdot {\sum\limits_{l = 1}^{L}{{c_{k}(l)}{\exp\left( {{j \cdot 2}\pi\quad f_{l}t} \right)}\quad{for}\quad n\quad T}}}} \leq t < {\left( {n + 1} \right)T}}} & (2)\end{matrix}$

A MC-CDMA receiver for a given user g has been illustrated schematicallyin FIG. 2. Since we consider here the downlink, the receiver is locatedin the mobile terminal.

After baseband demodulation, the signal is sampled at the “chip”frequency and the samples belonging to the guard interval areeliminated. The signal thus obtained can be written: $\begin{matrix}{{R_{g}(t)} = {{{\sum\limits_{k = 1}^{K}{d_{k} \cdot \sqrt{P\quad t_{k}} \cdot {\sum\limits_{l = 1}^{L}{{h_{g}(l)} \cdot {c_{k}(l)} \cdot {\exp\left( {{j \cdot 2}\pi\quad f_{l}t} \right)}}}}} + {{b(t)}{for}\quad n\quad T}} \leq t < {\left( {n + 1} \right)T}}} & (3)\end{matrix}$where t takes successive sampling time values, K is the number of usersand h_(g)(l) represents the response of the downlink channel of the userg to the frequency of the subcarrier l of the MC-CDMA symbol transmittedat time n.T and where b(t) is the received noise.

The samples obtained by sampling the demodulated signal at the “chip”frequency are serial to parallel converted in the serial to parallelconverter 210 _(g) before undergoing an FFT in the module 220 _(g). Thesamples in the frequency domain, output from 220 _(g), are despread bythe spreading sequence of user g and equalised so as to compensate forthe dispersive effects of the downlink transmission channel. To do this,the samples of the frequency domain are multiplied (by the multipliers230 ₁ ^(g), . . . , 230 _(L) ^(g)) on one hand with the coefficientsc_(g)*(l) (where .* is the conjugation operation) and on the other handwith equalising coefficients q_(g)(l), l=1, . . . , L. Severalequalising methods are known from the prior art, among others:

-   -   MRC (Maximum Ratio Combining) equalisation according to which        q_(t)=h_(t)*    -   EGC (Equal Gain Combining) equalisation according to which        q_(t)=e^(−jφl) where h_(t)=ρ_(t)e^(−jφt)    -   ZF (Zero Forcing) equalisation where q_(t)=h_(t) ⁻¹    -   MMSE (Minimum Mean Square Error) equalisation where        $q_{l} = \frac{h_{l}^{*}}{{h_{l}}^{2} + \sigma^{2}}$        and ρ² is the noise variance on a carrier.

After multiplication, the samples are added in adder 240 _(g) to outputthe resulting signal r_(g): $\begin{matrix}{r_{g} = {{\sum\limits_{k = 1}^{K}{d_{k} \cdot \sqrt{P\quad t_{k}} \cdot \left( {\sum\limits_{l = 1}^{L}{{h_{g}(l)}{{q_{g}(l)} \cdot {c_{k}(l)} \cdot {c_{g}^{*}(l)}}}} \right)}} + {\sum\limits_{l = 1}^{L}{{q_{g}(l)} \cdot {c_{g}^{*}(l)} \cdot {n_{g}(l)}}}}} & (4)\end{matrix}$which can be reformulated as: $\begin{matrix}{r_{g} = {{{d_{g} \cdot \sqrt{P\quad t_{g}}}\left( {\sum\limits_{l = 1}^{L}{{h_{g}(l)}{q_{g}(l)}{{c_{g}(l)} \cdot {c_{g}^{*}(l)}}}} \right)} + {\underset{k \neq g}{\sum\limits_{k = 1}^{K}}{d_{k} \cdot \sqrt{P\quad t_{k}} \cdot \left( {\sum\limits_{l = 1}^{L}{{h_{g}(l)}{{q_{g}(l)} \cdot {c_{k}(l)} \cdot {c_{g}^{*}(l)}}}} \right)}} + {\sum\limits_{l = 1}^{L}{{q_{g}(l)} \cdot {c_{g}^{*}(l)} \cdot {n_{g}(l)}}}}} & (5)\end{matrix}$where n_(g)(l) are Gaussian noise samples relative to the differentcarriers.

The first term of expression (5) corresponds to the desired receivedsignal dedicated to user g, the second term correspond to MultipleAccess Interference (MAI) and the third term corresponds to residualnoise. The Multiple Access Interference stems from the fact that adownlink channel carries the signals to a plurality of users.

The resulting signal r_(g) is a decision variable which is detected indetector 250 _(g) for supplying an estimated symbol {circumflex over(d)}_(g). The detection implemented can be a hard or a soft detection(in the latter case detector 250 _(g) can simply be omitted). Withoutloss of generality, it is assumed in the following that a soft detectionis implemented and therefore that {circumflex over (d)}_(g)=r_(g).

The capacity of a MC-CDMA system is basically limited by Multiple AccessInterference. A possible way to combat MAI and consequently increase thesystem capacity is to use a spatial filtering technique to separate thelinks from or to different users. Spatial filtering is generallyobtained by using antenna arrays for forming a plurality of beams indifferent directions. It has been recently proposed to use antennaarrays in MC-CDMA systems, in particular for transmission as disclosedin the article by M. Fujii entitled “Multibeam-time transmit diversityfor OFDM-CDMA” published in Proc. of Globecom 2001, vol. 25, pp.3095-3099 and in the article by C. K. Kim et al. entitled “Performanceanalysis of an MC-CDMA system with antenna array in a fading channel”,published in IEICE Trans. Commun. Vol. E83-B, N°1, January 2000, pp.84-92. However, when a user-specific spatial filtering technique is usedfor downlink transmission, in other words when a transmit beam is formedfor each user at the base station, the frequency separation of thedifferent users is not guaranteed anymore. In other words, although, onone hand, spatial filtering contributes to lower MAI by providingspatial separation of the transmission to the different users, it may,on the other hand, have a deleterious effect on the same MAI bydestroying the separation of the users in the frequency domain.

It is a first object of the present invention to propose a new filteringtechnique for MC-CDMA downlink transmission which minimises the MultipleAccess Interference for the different users of the system. Conversely,for a given MAI level, a second object of the present invention is toincrease the capacity of a MC-CDMA system.

Furthermore, as described above in connection with FIG. 2, the receivingprocess performed at a mobile terminal (MT) of a MC-CDMA system isrelatively complex since it involves in particular the determination ofthe equalising coefficients q_(g)(l) and the step of equalisationitself. A simplification of the receiving process is therefore desirableall the more since the computation and power resources at the MT sideare critically limited. A third object of the invention is to reduce thecomplexity of the receiving process at a mobile terminal withoutsacrificing the quality of service.

The above mentioned objects are attained by the transmitting method ofthe invention as defined in claim 1. Advantageous embodiments of theinvention are defined in the appended dependent claims.

The advantages and characteristics of the invention will emerge from areading of the following description given in relation to theaccompanying figures, amongst which:

FIG. 1 depicts schematically the structure of an MC-CDMA transmitterknown from the state of the art;

FIG. 2 depicts schematically the structure of an MC-CDMA receiver knownfrom the state of the art;

FIG. 3 depicts schematically the structure of an MC-CDMA transmitteraccording to the invention;

FIG. 4 depicts schematically the structure of a first MC-CDMA receiverto be used with the MC-CDMA transmitter according to a first embodimentof the invention;

FIG. 5 depicts schematically the structure of a second MC-CDMA receiverto be used with the MC-CDMA transmitter according to a second embodimentof the invention.

We refer back again to the context of a MC-CDMA system comprising a basestation transmitting a plurality of symbols to a plurality K of activeusers k=1, . . . , K sharing the same carriers of an OFDM multiplex.

The basic idea underlying the invention is to use a filtering techniqueat the transmission side which is jointly optimised in space andfrequency for all the active users. More specifically, if an array of Mantennas is used at the base station, the signal transmitted to user kby antenna m can be expressed as: $\begin{matrix}{{S_{k}^{m}(t)} = {d_{k} \cdot \sqrt{P\quad t_{k}} \cdot {\sum\limits_{l = 1}^{L}{{{w_{k}^{*}\left( {l,m} \right)} \cdot {c_{k}(l)}}{\exp\left( {{j \cdot 2}\pi\quad f_{l}t} \right)}}}}} & (6)\end{matrix}$where w_(k)*(l,m) is a complex weighting coefficient associated with theuser k, the frequency component l, the antenna m and .* denotes theconjugation operation. The components of the vector w_(k)*(l,m) can begrouped into a plurality of L spatial filtering vectors w_(k)*(l), l=1,. . . , L, each vector w_(k)*(1) being used by the antenna array to forma transmit beam for the frequency component l of user k.

If we assume that the signals transmitted by the base station to the Kusers are synchronous, the signal transmitted to all the users byantenna m can be simply expressed as: $\begin{matrix}{{S^{m}(t)} = {\sum\limits_{k = 1}^{K}{d_{k} \cdot \sqrt{P\quad t_{k}} \cdot {\sum\limits_{l = 1}^{L}{{{w_{k}^{*}\left( {l,m} \right)} \cdot {c_{k}(l)}}{\exp\left( {{j \cdot 2}\pi\quad f_{l}t} \right)}}}}}} & (7)\end{matrix}$

FIG. 3 illustrates schematically a MC-CDMA transmitter using the spatialfiltering method according to the invention. The transmitter comprises Kidentical branches, each branch corresponding to a given active user.The branch dedicated to user k comprises a multiplier 310 _(k), ademultiplexer 320 _(k) and a parallel multiplier 330 _(k) connected inseries. For example, the branch dedicated to user 1 illustrated in theupper part of the Fig. comprises a multiplier 310 ₁ for multiplying thecomplex value {square root}{square root over (Pt_(I))}.d₁ (it isrecalled that d₁ is the symbol to be transmitted to user 1) with thespreading sequence c₁(l), a demultiplexer 320 ₁ for serial-to-parallelconverting the spread complex values, a parallel multiplier 330 ₁ formultiplying each of the spread complex values {square root}{square rootover (Pt₁)}.d₁.c₁(l) with components of a complex weighting vector w₁*as defined further below. The result of the parallel multiplication in330 ₁ is represented by the M vectors z₁ ¹, . . . , z₁ ^(M) each vectorz₁ ^(m) being constituted of the frequency components of the signal tobe transmitted by the antenna 370 _(m). More specifically, z₁ ^(m), m=1,. . . , M is defined as a L-dimension vector (z₁ ^(m)(l), . . . ,z₁^(m)(L))^(T) where z₁ ^(m)(l)={square root}{square root over(Pt₁)}.d₁.c₁(l)w₁*(l,m). Similarly, the output of the parallelmultiplier 330 _(k) of the k^(th) branch is constituted of M vectorsz_(k) ¹, . . . ,z_(k) ^(M) the elements of which are given by z_(k)^(m)(l)={square root}{square root over(Pt_(k))}.d_(k).c_(k)(l)w_(k)*(l,m).

For a given user k the complex weighting coefficients w_(k)*(l,m) aregrouped into a vector w_(k) of size M·L defined as w_(k)*=(w_(k)*(1,1),. . . , w_(k)*(L,1), . . . , w_(k)*(1,M), . . . , w_(k)*(L,M))^(T), thefirst L elements of which corresponding to the weighting coefficientsfor antenna 1, user k and subcarriers 1 to L, the second L elements ofwhich corresponding to the weighting coefficients for antenna 2, user kand subcarriers 1 to L, and so on. As the coefficients w_(k)*(l,m) areapplied both in the space domain (for a given subcarrier l, they can beregarded as forming a beam for user k) and in the frequency domain (fora given antenna m, the coefficients w_(k)*(l,m) can be regarded as thoseof conventional frequency filter), the vector w_(k)* will be hereinafterreferred to as the space-frequency transmit filtering (SFTF) vectorassociated to user k.

The MC-CDMA transmitter is further provided with a plurality M of adders340 ₁, . . . , 340 _(M), each adder 340 _(m) adding the signal vectorsz₁ ^(m), . . . , z_(K) ^(m), m=1, . . . , M output by the parallelmultipliers 330 ₁, . . . , 330 _(M) and supplying the resulting vectorsto the modules 350 ₁, . . . , 350 _(M) respectively. More precisely,each module 350 _(m) (identical to the module 130 _(k) in FIG. 1)performs an inverse Fast Fourier Transform on the vector of compoundfrequency components$\left( {{\sum\limits_{k = 1}^{K}{z_{k}^{m}(1)}},\ldots\quad,{\sum\limits_{k = 1}^{K}{z_{k}^{m}(L)}}} \right)^{T}$and adds a prefix (Δ) to the MC-CDMA symbol thus obtained. Afterparallel-to-serial conversion in 360 ₁ (and frequency up-conversion, notshown), the signal S^(m)(t) carrying the MC-CDMA symbol is transmittedby the antenna 370 _(m).

As described further below, the SFTF vectors w_(k)*, k=1, . . . , K, orequivalently the weighting coefficients w_(k)*(l,m), l=1, . . . , L;m=1, . . . , M are determined by a calculation module 380 from estimatesof the coefficients of the downlink transmission channels and suppliedto the parallel multipliers 330 ₁, . . . , 330 _(K). It is assumed inthe following that the transmission is free from inter-carrierinterference and inter-symbol interference (the latter, thanks to prefixinsertion). In such instance, the downlink transmission channel betweenantenna m of the base station and the mobile terminal of user k can becharacterised by a single multiplicative complex coefficient h_(k)(l,m)(hereinafter called channel coefficient) for each subcarrier l. Thecoefficients h_(k)(l,m) are assumed identical for the downlink and theuplink channels, assumption which is verified in practice when theMC-CDMA system operates in TDD (Time Division Duplex) mode. Theestimates of the channel coefficients are hereinafter denotedĥ_(k)(l,m).

The channel coefficients h_(k)(l,m) depend on the spatial signature ofthe downlink multipath channel and the fading coefficient of thechannel. The spatial signature of the channel (supposed identical fordownlink and uplink) is defined by the directions of transmission of thesignal to user k or, equivalently by the direction of arrival (DOAS) ofthe signal transmitted by user k to the base station. It should beunderstood that the coefficients h_(k)(l,m) for a given user k reflectnot only the directivity pattern of the (transmit or receive) beam forthis user at the various subcarrier frequencies but also the fading ofthe transmission channel at these frequencies.

If we now consider a mobile terminal of a given user g having thestructure illustrated in FIG. 2 and receiving a signal transmitted bythe MC-CDMA of FIG. 3, the decision variable can be expressed as,similar to (4): $\begin{matrix}{{\hat{d}}_{g} = {{\sum\limits_{k = 1}^{K}{d_{k} \cdot \sqrt{P\quad t_{k}} \cdot {\sum\limits_{m = 1}^{M}{\sum\limits_{l = 1}^{L}{{w_{k}^{*}\left( {l,m} \right)} \cdot {h_{g}\left( {l,m} \right)} \cdot {q_{g}(l)} \cdot {c_{k}(l)} \cdot {c_{g}^{*}(l)}}}}}} + {\sum\limits_{l = 1}^{L}{{q_{g}(l)}{{c_{g}^{*}(l)} \cdot {n_{g}(l)}}}}}} & (8)\end{matrix}$which can be reformulated as follows: $\begin{matrix}\begin{matrix}{{\hat{d}}_{g} = {{{d_{g} \cdot \sqrt{{Pt}_{g}}}\left( {\sum\limits_{m = 1}^{M}{\sum\limits_{l = 1}^{L}{{h_{g}\left( {l,m} \right)} \cdot {w_{g}^{*}\left( {l,m} \right)} \cdot {c_{g}(l)} \cdot {e_{g}^{*}(l)}}}} \right)} +}} \\{{\sum\limits_{m = 1}^{M}{\sum\limits_{l = 1}^{L}{{h_{g}\left( {l,m} \right)} \cdot {e_{g}^{*}(l)} \cdot \left( {\sum\limits_{\underset{k \neq g}{k = 1}}^{K}{d_{k} \cdot \sqrt{{Pt}_{k}} \cdot {w_{k}^{*}\left( {l,m} \right)} \cdot {c_{k}(l)}}} \right)}}} +} \\{\sum\limits_{l = 1}^{L}{{e_{g}^{*}(l)} \cdot {n_{g}(l)}}}\end{matrix} & (9)\end{matrix}$where n_(g)(l) are Gaussian noise samples relative to the differentcarriers and e_(g)(l)=q_(g)*(l)c_(g)(l) where the coefficients q_(g)(l)are not necessarily determined by one of the equalising methods recitedabove and can take any value. It should be noted that e_(g)(l) are theconjugates of the coefficients combining the components carried by thedifferent subcarriers at the output of the FFT module 220 _(g). As itwill be apparent to the man skilled in the art, the first term ofexpression (9) corresponds to the desired signal, the second termcorresponds to the multiple access interference and the final termcorresponds to the residual noise after despreading.

The expression (9) can be equivalently formulated in a more conciseform: $\begin{matrix}\begin{matrix}{{\hat{d}}_{g} = {{{\overset{\sim}{e}}_{g}^{H} \cdot \left( {h_{g} \circ w_{g}^{*} \circ {\overset{\sim}{c}}_{g\quad}} \right) \cdot d_{g} \cdot \sqrt{{Pt}_{g}}} +}} \\{{\overset{\sim}{e}}_{g}^{H} \cdot \left( {{h_{g} \circ \left( {\sum\limits_{\underset{k \neq g}{k = 1}}^{K}{\left( {w_{k}^{*} \circ {\overset{\sim}{c}}_{k}} \right) \cdot d_{k} \cdot \sqrt{{Pt}_{k}}}} \right)} + {e_{g}^{H} \cdot n_{g}}} \right.}\end{matrix} & (10)\end{matrix}$where the boldface letters represent vectors and:

-   -   {tilde over (c)}_(k) is a vector of size M·L defined as {tilde        over (c)}_(k)=(c_(k) ^(T),c_(k) ^(T), . . . , c_(k) ^(T))^(T)        i.e. is the concatenation of M times the vector c_(k)=(c_(k)(l),        . . . , c_(k)(L))^(T) representing the spreading sequence for        user k;    -   {tilde over (e)}_(g) is a vector of size M·L defined as {tilde        over (e)}_(g)=(e_(g) ^(T),e_(g) ^(T), . . . , e_(g) ^(T))^(T)        i.e. is the concatenation of M times the vector e_(g)=(e_(g)(l),        . . . , e_(g)(L))^(T), or, equivalently, {tilde over        (e)}_(g)={tilde over (c)}_(g)o{tilde over (q)}_(g) where {tilde        over (q)}_(g)=(q_(g) ^(T),q_(g) ^(T), . . . , q_(g) ^(T))^(T) is        the concatenation of M times the vector q_(g)=(q_(g)(1), . . . ,        q_(g)(L))^(T).    -   h_(g) is a vector of size M·L defined as h_(g)=(h_(g)(l,l), . .        . , h_(g)(L,1), . . . , h_(g)(1,M), . . . , h_(g)(L,M))^(T) the        first L elements of which corresponding to the channel between        antenna 1 and user g, the second L elements of which        corresponding to the channel between antenna 2 and user g and so        on;    -   w_(k)* is the SFTF vector relative to user k as defined above;    -   e_(g) and n_(g) are respectively defined as e_(g)=(e_(g)(1), . .        . , e_(g)(L))^(T) and n_(g)=(n_(g)(1), . . . , n_(g)(L))^(T);    -   (.)^(H) denotes the hermitian transpose operator, u.v denotes        the scalar product of vectors u and v, u×v denotes the element        wise product of vectors u and v, i.e. the i^(th) element of        vector u×v is the product of the i^(th) element of vector u and        the i^(th) element of vector v.

According to a first advantageous aspect of the invention, for a givenuser g, a set of weighting coefficients w_(g)*(l,m), l=1, . . . , L;m=1, . . . , M (or equivalently a SFTF vector w_(g)*) is determined toensure a minimisation of the MAI affecting the user in question, takinginto account the global effect resulting from the MAI reduction inducedby the separation of the active users in the space domain and the MAIincrease induced by the loss of orthogonality in the frequency domain.

According to a second advantageous aspect of the invention, there isperformed a joint MA′ minisation criterion taking into account all theactive users. More precisely, the proposed minimisation criterion is notaimed at merely minimising the MAI affecting the reception of a givenactive user irrespective of the MAI affecting the reception of the otheractive users but takes also into account the MAIs affecting the latterusers induced by the signal transmitted to the user in question.

According to a third advantageous aspect of the invention, there is useda MAI minimisation criterion taking into account the transmit powerconstraint of the MC-CDMA transmitter, which is itself inherentlylimited by the total transmit power of the base station.

In order to explain in further detail the transmission method accordingto the invention, we consider first a criterion based on themaximisation of the signal to interference plus noise ratio (SINR)relative to a given active user g, under the constraint of a fixedtransmit power level for this user.

The signal to interference plus noise ratio relative to the user g canbe expressed as: $\begin{matrix}{{SINR}_{g} = \frac{P_{g}}{{MAI}_{g} + \sigma^{2}}} & (11)\end{matrix}$where P_(g) is the power of the desired signal received by user g,MAI_(g) is the MAI level affecting the desired signal and ρ² is varianceof the residual noise after despreading.

From the first term of (10) and assuming that the average power of thesymbols d_(g) is unity, the power of the desired signal received by userg can be expressed as:P _(g) =Pt _(g) ×|w _(g) ^(H)×({tilde over (e)}_(g)*×h_(g) ×{tilde over(c)} _(g))|²   (12)

From the second term of (10) and assuming that the average power of thesymbols d_(k) is unity, the multiple access interference level MAI_(g)can be expressed as: $\begin{matrix}{{MAI}_{g} = {\sum\limits_{\underset{k \neq g}{k = 1}}^{K}{{Pt}_{k} \cdot {p_{MAI}\left( {k->g} \right)}}}} & (13)\end{matrix}$where P_(MAI)(k→g) reflects the normalised contribution of (the signaltransmitted to) user k to the MAI affecting user g and is defined as:P _(MAI)(k→g)=w _(k) ^(H) v _(gk) v _(gk) ^(H) w _(k)   (14)where v_(gk)={tilde over (e)}_(g)*×h_(g)×{tilde over (c)}_(k)={tildeover (c)}_(g)×{tilde over (c)}_(k)={tilde over (c)}_(g)×{tilde over(q)}_(g)×h_(g)×{tilde over (c)}_(k).

From (12), (13) and (14), the signal to interference plus noise ratiorelative to user g can be rewritten: $\begin{matrix}{{SINR}_{g} = \frac{{Pt}_{g}{{w_{g}^{H} \cdot \left( {{\overset{\sim}{e}}_{g}^{*} \circ h_{g} \circ {\overset{\sim}{c}}_{g}} \right)}}^{2}}{{\sum\limits_{\underset{k \neq g}{k = 1}}^{K}{{{Pt}_{k} \cdot w_{k}^{H}}v_{gk}v_{gk}^{H}w_{k}}} + \sigma^{2}}} & (15)\end{matrix}$

As it is apparent from (15), the expression of SINR_(g) does not dependonly upon the weighting coefficients w_(g)*(l,m) relative to user g(i.e. the SFTF vector w_(g)* relative to user g) but also upon theweighting coefficients relative to the other users kg (i.e the SFTFvectors w_(k)* relative to the users k≈g). This can be attributed to thefact that the MAI affecting user g is influenced by the distribution inspace and frequency of the signals transmitted to the other users k≈g.In other words, a change of the SFTF vector relative to a given usermodifies the SINRs of all the other active users. It follows that theproblem of finding the SFTF vector w_(g)* maximising the SINR_(g) cannotbe solved independently of the problem of finding the other SFTF vectorw_(k)* maximising the values SINR_(k) for k≈g. However, finding the setof the SFTF vectors w_(k)* maximising simultaneously all the valuesSINR_(k) is a very complex if not intractable task.

According to the invention, the problem of maximising the SINR_(g) iselegantly solved by observing that in practice the channel responsevectors h_(k), k=1, . . . ,K have the same statistical properties andthat consequently for two given users k and k′ the nornalisedinterference contributions P_(MAI)(k→k′) and P_(MAI)(k′→k) can beconsidered equal, which is especially justified when the same method ofspace-time filtering is applied to all the users.

More precisely, there is proposed a criterion based upon a pseudo signalto noise plus interference ratio denoted SINR_(g) ^(m) and defined asfollows: $\begin{matrix}{{{SINR}_{g}^{m} = {\frac{P_{g}}{{MAI}_{g}^{m} + \sigma^{2}}\quad{where}}}{{MAI}_{g}^{m} = {\sum\limits_{\underset{k \neq g}{k = 1}}^{K}{{{Pt}_{k} \cdot {p_{MAI}\left( {g->k} \right)}}\quad{with}}}}{{{p_{MAI}\left( {g->k} \right)} = {w_{g}^{H}v_{kg}v_{kg}^{H}w_{g}}},{{that}\quad\text{is:}}}{{MAI}_{g}^{m} = {{{w_{g}^{H}\left( {\sum\limits_{\underset{k \neq g}{k = 1}}^{K}{{{Pt}_{k} \cdot v_{kg}}v_{kg}^{H}}} \right)}w_{g}} = {w_{g}^{H}\Phi_{g}w_{g}}}}{{where}\quad\Phi_{g}\quad{is}\quad{the}\quad{quadratic}\quad{matrix}\quad{defined}\quad\text{as:}}{\Phi_{g} = {\sum\limits_{\underset{k \neq g}{k = 1}}^{K}{{{Pt}_{k} \cdot v_{kg}}{v_{kg}^{H}.}}}}} & (16)\end{matrix}$

The pseudo signal to noise plus interference ratio can therefore bereformulated as: $\begin{matrix}{{SINR}_{g}^{m} = \frac{{Pt}_{g}{{w_{g}^{H} \cdot \left( {{\overset{\sim}{e}}_{g}^{*} \circ h_{g} \circ {\overset{\sim}{c}}_{g}} \right)}}^{2}}{{w_{g}^{H}\Phi_{g}w_{g}} + \sigma^{2}}} & (17)\end{matrix}$

For a fixed predetermined transmit power value Pt_(g), the constraint onthe transmit power for user g can be expressed as a constraint on themodule of the SFTF vector w_(g), namely W_(g) ^(H).w_(g)=1.

From (17), the maximisation of SINR_(g) ^(m) under the constraint of afixed transmit power is equivalent to find: $\begin{matrix}{{\arg\quad\max} = \frac{{Pt}_{g}{{w_{g}^{H} \cdot \left( {{\overset{\sim}{e}}_{g}^{*} \circ h_{g} \circ {\overset{\sim}{c}}_{g}} \right)}}^{2}}{{w_{g}^{H}\left( {\Phi_{g} + {\sigma^{2}I_{ML}}} \right)}w_{g}}} & (18)\end{matrix}$under the constraint w_(g) ^(H).w_(g)=1, where I_(ML) is the identitymatrix of size M·L×M·L.

It should be noted that expression (18) depends only on the SFTF vectorw_(g) and is invariant by multiplication of w_(g) with a constant.Defining {haeck over (w)}_(g)=βw_(g), where β is a scalar, it is therepossible to look for the optimal vector {haeck over (w)}_(g) thatverifies {haeck over (w)}_(g) ^(H)({tilde over (e)}_(g)*×h_(g)×{tildeover (c)}_(g))=1, and then to normalise the result by the factor$\frac{1}{{\overset{\Cup}{w}}_{g}}$in order to obtain w_(g). The optimum pre-distortion vector SFTF {haeckover (w)}_(g) must therefore satisfy:arg min({haeck over (w)}_(g) ^(H)ψ_(g){haeck over (w)}_(g)) withψ_(g)=φ_(g)+ρ²·I_(ML) and {haeck over (w)}_(g) ^(H)({tilde over(e)}_(g)*×h_(g)×{tilde over (c)}_(g))=1   (19)

For solving this problem, we introduce the Lagrange function:£={haeck over (w)}_(g) ^(H)Ψ_(g) {haeck over (w)} _(g)−λ({haeck over(w)} _(g) ^(H) f _(g)−1) with f _(g) ={tilde over (e)} _(g) *·h _(g)·{tilde over (c)} _(g)   (20)where λ is a Lagrange multiplier.

By calculating the gradient according to the vectors {haeck over(w)}_(g)* (the same result can be obtained by calculating the gradientaccording to the vector {haeck over (w)}_(g)):V _({haeck over (w)}) _(R) *£=Φ _(g) {haeck over (w)} _(g) −λf _(g)=0  (21)Finally, we tan conclude that the optimal SFTF vector {haeck over(w)}_(g) is given by:{haeck over (w)} _(g)=λ(Φ_(g)+σ² .I _(ML))⁻¹ f _(g)=λ(Φ_(g)+σ² .I _(ML))⁻¹({tilde over (e)} _(g)*×h_(g) ×{tilde over (e)} _(g))   (22)

The SFTF vector w_(g) can be obtained from {tilde over (w)}_(g):w _(g)=μ_(g)(Φ_(g)+σ² .I _(ML))⁻¹({tilde over (c)} _(g) *×{tilde over(q)} _(g) ×h _(g) ×{tilde over (c)} _(g))   (23)where the coefficient μ_(g) is given by the constraint upon the transmitpower for user g, namely is chosen so that w_(g) ^(H)·w_(g)=1.

In practice, the downlink channel coefficients h_(g) (e, m) constitutingthe vector h_(g) are assumed identical to the corresponding uplinkchannel coefficients, which are in turn estimated from pilot symbolstransmitted from the active users to the base station.

Turning back to FIG. 3 and denoting ĥ_(k) the vector of the estimatesĥ_(k)(l, m), the calculation module 380 determines for each active userk the SFTF vector w_(k)* from:w _(k)=μ_(k)({circumflex over (Φ)}_(k)+σ² .I _(ML))⁻¹({tilde over (c)}_(k) ×{tilde over (q)} _(k) ×{tilde over (h)} _(k) ×{tilde over (c)}_(k))   (24)where the coefficient μ_(k) is given by the constraint upon the transmitpower for user k (i.e. w_(k) ^(H)·w_(k)=1) and $\begin{matrix}{{\hat{\Phi}}_{k} = {{\sum\limits_{\underset{k^{\prime} \neq k}{k = 1}}^{K}{{Pt}_{k^{\prime}}{\hat{v}}_{k^{\prime}k}{\hat{v}}_{k^{\prime}k}^{H}\quad{with}\quad v_{k^{\prime}k}}} = {{\overset{\sim}{c}}_{k^{\prime}}^{*} \circ {\overset{\sim}{q}}_{k^{\prime}} \circ {\hat{h}}_{k^{\prime}} \circ {\overset{\sim}{c}}_{k}}}} & (25)\end{matrix}$

According to first embodiment of the invention, the SFTF vector w_(g)*for a given user g is determined by the calculation module 380 from:w _(g)=μ_(g)({circumflex over (Φ)}_(g)+σ² .I _(ML))⁻¹({tilde over (c)}_(g) *×ĥ _(g) ×ĉ _(g))   (26)which can be further simplified if the spreading sequences are such thatc_(g)(l).c_(g)*(l)=1 for l=1, . . . , L e.g. if Walsh-Hadamard spreadingsequences (c_(g)(l)ε{−1,1}) are used:w _(g)=μ_(g)({circumflex over (Φ)}_(g)+σ² .I _(ML))⁻¹ ĥ _(g)   (27)

In such instance, the receiving process carried out at the mobileterminals can be drastically simplified as shown in FIG. 4. The MC-CDMAreceiver for a user g is schematically represented in FIG. 4 andcomprises modules 410 _(g) to 450 _(g) identical to the correspondingmodules 210 _(g) to 250 _(g) of FIG. 2. However, in contrast with theMC-CDMA receiver of the prior art (FIG. 2), a simple despreading iseffected at the output of the FFT module 420 _(g) and no equalisation isrequired anymore. In particular, an estimation of the downlink channelcoefficients is not needed at the receiver side, thus relieving themobile terminal of the computation burden associated therewith.

It should be appreciated that the filtering in the frequency domainperformed at the transmission side by the weighting coefficients of SFTFvector w_(g)* fully or almost fully pre-compensates for the fading onthe carriers of the downlink transmission channel.

According to a second embodiment of the invention, the downlink channelcoefficients h_(g)(l,m) are coarsely estimated by the MC-CDMAtransmitter and a complementary equalisation is performed at thereceiving side.

This is for example the case if the estimates of the uplink channelcoefficients (from which the latter are derived) are updated at a ratelower than the actual variation thereof More specifically, denotingĥ_(g) ^(C) the vector representing the coarse estimates of the channelcoefficients for a given user g, the MC-CDMA transmitter would apply aSFTF filtering based on:w _(g)=μ_(g)({circumflex over (Φ)}_(g)+σ² .I _(ML))⁻¹({tilde over (c)}_(g)*×ĥ_(g) ^(C) ×{tilde over (c)} _(g))   (28)and a set of equalising coefficients q_(g) ^(f)(l), l=1, . . . L wouldfinely compensate for the residual frequency distortion at the receivingside.

In a further variant, the vector of coarse estimates, ĥ_(g) ^(C), usedfor determining w_(g)* in the calculation module 380, is derived fromthe spatial signature of user g More specifically, it is assumed thatthe channel coefficients h_(g)(l, m) can be decomposed into:h _(g)(l,m)={overscore (h)} _(g)(l,m)η_(g)(l)   (29)where {overscore (h)}_(g)(l,m) accounts for the spatial signature ofuser g (varying relatively slowly in time) and η_(g)(l) accounts for thefrequency fading of the channel. The MC-CDMA transmitter estimates thecoefficients {overscore (h)}_(g)(l,m) from the DOAs of the signalreceived by the antenna array from user g and uses these estimates{overscore (h)}_(g)(l,m) as elements of the vector ĥ_(g) ^(C).

FIG. 5 shows schematically a receiver for use with a MC-CDMA transmitteraccording to the latter variant. The modules 510 _(g) to 550 _(g) areidentical to the corresponding modules 210 _(g) to 250 _(g) of FIG. 2and the compensation for the fast fading factors η_(g)(l) is ensuredhere by equalising coefficients q_(g) ^(f)(l), l=1, . . . L derived fromη_(g)(l) according to one of the known types of equalisation method.

A further advantageous aspect of the invention lies in the possibilityof increasing the capacity of a MC-CDMA system. It is reminded that thecapacity of a conventional MC-CDMA system is limited by the number ofavailable spreading codes (or spreading sequences), which is equal tothe number L of subcarriers when the codes are chosen orthogonal. Theuser separation in the space domain provided by the transmission methodaccording to the invention allows to reuse the same spreading codes fordifferent users. More specifically, a spreading code c_(k)(l), l=1, . .. , L already allocated to a user k can be also reallocated to a user k′provided users k and k′ have substantially different spatial signatures.5 According to a first possible allocation scheme, if the number ofactive users happens to exceed the number L of available spreading codes(for example, if the available spreading codes are already allocated andif an incoming call is requested), the spreading codes are reallocatede.g in the natural order c₁,c₂, . . . , so that two users k and k+Lshare the same spreading code c_(k). In order to reduce the interferenceoccurring when users k and k+L exhibit similar spatial signatures, it isfurther proposed to apply random scrambling codes on top of theavailable spreading codes. More specifically, if a symbol has to betransmitted to a user k belonging to a given set Ω_(p), where pε{1, . .. ,P}, it is multiplied by the following sequence:c _(k) ^(ext)(l)=c _(k[L)](l)·m _(p)(l), l=1, . . . L   (30)where user index k may be greater than L, p denotes the integer part ofthe division k/L and k[L] denotes the rest thereof, c_(k) ^(ext)(l),l=1, . . . ,L stands for a spreading sequence belonging to an extendedset (of cardinal L·P) and m_(p)(l), l=1, . . . ,L is a random scramblingcode.

Since users belonging to a given set Ω_(p) are subjected to the samescrambling code, their respective spreading sequences (as defined in(30)) are orthogonal and, consequently, these users are spatially andfrequency separated by the transmission method according to theinvention. In contrast, orthogonality is not maintained betweenspreading sequences allocated to users belonging to different sets.However, the latter users still benefit from the spatial separationprovided by said transmission method as well as from the interferencereduction due to the random scrambling .

Although the MC-CDMA transmitter illustrated in FIG. 3 has beendescribed in terms of functional modules e.g. computing or estimatingmeans, it will be appreciated by the man skilled in the art that all orpart of this device can be implemented by means of a single processoreither dedicated for performing all the functions depicted or in theform of a plurality of processors either dedicated or programmed foreach performing one or some of said functions.

1) Transmission method for transmitting a plurality of symbols from abase station of a MC-CDMA telecommunication system to a plurality (K) ofusers, each symbol (d_(k)) to be transmitted to a user being spread witha coding sequence (c_(k)(l) ) over a plurality (L) of carriers (l) toproduce a plurality of corresponding frequency components, said basestation being provided with a plurality (M) of antenna elements,characterised in that each frequency component produced by a symbol of auser (k) is weighted by a plurality (M) of weighting complexcoefficients (w_(k)*(l,m),m=1, . . . ,M) to obtain a plurality (LM) ofweighted frequency components (z_(k) ^(m)(l)), each weightingcoefficient being relative to a user (k), a carrier (l) and an antennaelement (m) and said plurality of weighting coefficients beingdetermined from estimates of the channel coefficients (h_(k)(l,m)) ofthe downlink transmission channels between each antenna element and eachuser for each carrier frequency. 2) Transmission method according toclaim 1, characterised in that, for each antenna element (m) theweighted frequency components relative to said antenna element and tothe different users are added up per carrier to output a plurality (L)of compound frequency components$\left( {{\sum\limits_{k = 1}^{K}\quad{z_{k}^{m}(l)}},{l = 1},\ldots,L} \right),$said plurality of compound frequency components being further subjectedto an inverse Fourier transform to generate a signal (S^(m)(t)) to betransmitted by said antenna element. 3) Transmission method according toclaim 1 or 2, characterised in that said estimates of the channelcoefficients are obtained as estimates of the channel coefficients ofthe uplink transmission channels between each user and each antennaelement for each carrier frequency. 4) Transmission method according toclaim 3, characterised in that the weighting coefficients relative to agiven user are obtained as a function of the coding sequences of allsaid users, said estimates of channel coefficients, the transmit powers(Pt_(k)) used for respectively transmitting said symbols to thedifferent users, a variance of noise (σ²) affecting the receivedfrequency components at the user side and equalising coefficientsapplied thereto. 5) Transmission method according to claim 4characterised in that the weighting coefficients relative to a givenuser g are determined from the elements of a vector w_(g)* where .*denotes the conjugate operation and where w_(g) is determined accordingto an expression of the type:w _(g)=μ_(g)({circumflex over (Φ)} _(g)+σ² .I _(ML))⁻¹({tilde over (c)}_(g) *×{tilde over (q)} _(g) ×{tilde over (h)} _(g) ×{tilde over (c)}_(g)) where, M and L being respectively the number of antenna elementsand the number of carriers; {tilde over (c)}_(g) is a vector of size M·Ldefined as the concatenation of M times the vector c_(g)=(c_(g)(1), . .. ,c_(g)(L)^(T) representing the coding sequence of said given user g;{tilde over (q)}_(g) is a vector of size M·L defined as theconcatenation of M times the vector q_(g)=(q_(g)(l), . . . ,q_(g)(L)^(T)representing the equalising coefficients for said given user g; ĥ_(g) isa vector of size M·L the first L elements of which represent the saidestimates of the channel between antenna element 1 and user g, thesecond L elements of which corresponding to the channel between antennaelement 2 and user g and so on; μ_(g) is a scalar coefficient given bythe constraint upon the transmit power for user g; I_(ML) is theidentity matrix of size M·L×M·L; σ² is the value of said noise variance;{circumflex over (Φ)}_(g) is a hermitian matrix characterising themultiple access interference generated by user g on the other users; andwhere .×. denotes the element by element multiplication of two vectors.6) Transmission method according to claim 5 characterised in that saidhermitian matrix is obtained from an expression of the type:${\hat{\Phi}}_{g} = {\sum\limits_{k \neq {1g}}^{K}\quad{{{Pt}_{k} \cdot {\hat{v}}_{kg}}{\hat{v}}_{kg}^{H}}}$where K is number of users, Pt_(k) is the transmit power for user k and{circumflex over (v)} _(kg) ={tilde over (c)} _(k) ×{tilde over (q)}_(k) ×{tilde over (h)} _(k) ×{tilde over (c)} _(g) where {tilde over(c)}_(k) is a vector of size M·L defined as the concatenation of M timesthe vector c_(k)=(c_(k)(1), . . . ,c_(k)(L)^(T) representing the codingsequence of user k; {tilde over (q)}_(k) is a vector of size M·L definedas the concatenation of M times the vector q_(k)=q_(k)(1), . . . ,q_(k)(L)^(T) representing the equalising coefficients for user k. ĥ_(k)is a vector of size M·L the first L elements of which represent the saidestimates of the channel between antenna element 1 and user k, thesecond L elements of which corresponding to the channel between antennaelement 2 and user k and so on. 7) Transmission method according toclaim 4 characterised in that the weighting coefficients relative to agiven user g are determined from the elements of a vector w_(g)* where.* denotes the conjugate operation and where w_(g) is determinedaccording to an expression of the type:w _(g)=μ_(g)({circumflex over (Φ)}_(g)+σ² .I _(ML))⁻¹({tilde over (c)}_(g) ×ĥ _(g) ×{tilde over (c)} _(g)) where, M and L being respectivelythe number of antenna elements and the number of carriers; {tilde over(c)}_(g) is a vector of size M·L defined as the concatenation of M timesthe vector c_(g)=(c_(g)(1), . . . , c_(g)(L))^(T) representing thecoding sequence of said given user g; ĥ_(g) is a vector of size M·L thefirst L elements of which represent the said estimates of the channelbetween antenna element 1 and user g, the second L elements of whichcorresponding to the channel between antenna element 2 and user g and soon; μ_(g) is a scalar coefficient given by the constraint upon thetransmit power for user g; I_(ML) is the identity matrix of sizeM·L×M·L; σ² is the value of said noise variance; {circumflex over(Φ)}_(g) is a hermitian matrix characterising the multiple accessinterference generated by user g on the other users; and where .×.denotes the element by element multiplication of two vectors. 8)Transmission method according to claim 4 characterised in that theweighting coefficients relative to a given user g are determined fromthe elements of a vector w_(g)* where .* denotes the conjugate operationand where w_(g) is determined according to an expression of the type:w _(g)=μ_(g)({circumflex over (Φ)}_(g)σ² .I _(ML))⁻¹ ĥ _(g) where, M andL being respectively the number of antenna elements and the number ofcarriers; ĥ_(g) is a vector of size M·L the first L elements of whichrepresent the said estimates of the channel between antenna element 1and user g, the second L elements of which corresponding to the channelbetween antenna element 2 and user g and so on; μ_(g) is a scalarcoefficient given by the constraint upon the transmit power for user g;I_(ML) is the identity matrix of size M·L×M·L; σ² is the value of saidnoise variance; {circumflex over (Φ)}_(g) is a hermitian matrixcharacterising the multiple access interference generated by user g onthe other users . 9) Transmission method according to claim 7 or 8,characterised in that said hermitian matrix is obtained from anexpression of the type:${\hat{\Phi}}_{g} = {\sum\limits_{k \neq {1g}}^{K}\quad{{{Pt}_{k} \cdot {\hat{v}}_{kg}}{\hat{v}}_{kg}^{H}}}$where K is number of users, Pt_(k) is the transmit power for user k and{circumflex over (v)}_(kg) ={tilde over (c)} _(k) ×ĥ _(k) ×{tilde over(c)} _(g) where {tilde over (c)}_(k) is a vector of size M·L defined asthe concatenation of M times the vector c_(k)=(c_(k)(1), . . . ,c_(k)(L))^(T) representing the coding sequence of user k, {tilde over(c)}_(g) is a vector of size M·L defined as the concatenation of M timesthe vector c_(g)=(c_(g)(1), . . . ,c_(g)(L))^(T) representing the codingsequence of said given user g; ĥ_(k) is a vector of size M·L the first Lelements of which represent the said estimates of the channel betweenantenna element 1 and user k, the second L elements of whichcorresponding to the channel between antenna element 2 and user k and soon; and where .×. denotes the element by element multiplication of twovectors.